Consider the following reaction occurring in the blast furnace. \(\mathrm{Fe}_{3} \mathrm{O}_{4(\mathrm{~s})}+4 \mathrm{CO}_{(\mathrm{g})} \rightarrow 3 \mathrm{Fe}_{(\mathrm{l})}+4 \mathrm{CO}_{2(\mathrm{~g})}\) ' \(x\) ' kg of iron is produced when \(2.32 \times 10^{3} \mathrm{~kg} \mathrm{Fe}_{3} \mathrm{O}_{4}\) and \(2.8 \times 10^{2} \mathrm{~kg} \mathrm{CO}\) are brought together in the furnace. The value of ' \(x\) ' is \_\_\_\_. (nearest integer) \{Given : Molar mass of \(\mathrm{Fe}_{3} \mathrm{O}_{4}=232 \mathrm{~g} \mathrm{~mol}^{-1}\) Molar mass of \(\mathrm{CO}=28 \mathrm{~g} \mathrm{~mol}^{-1}\) Molar mass of \(\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}\) \}

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Some Basic Concepts of Chemistry

Consider the following reaction occurring in the blast furnace.

Fe_{3} O_{4 (s)} + 4 CO_{(g)} \to 3 Fe_{(l)} + 4 CO_{2 (g)}

x

' kg of iron is produced when

2.32 \times 1 0^{3} kg Fe_{3} O_{4}

and

2.8 \times 1 0^{2} kg CO

are brought together in the furnace. The value of '

x

' is ____. (nearest integer)
{Given :
Molar mass of

Fe_{3} O_{4} = 232 g mol^{- 1}

Molar mass of

CO = 28 g mol^{- 1}

Molar mass of

Fe = 56 g mol^{- 1}

}

Answer: 420

F e_{3} O_{4} (s) + 4 C O (g) \to 3 F e (l) + 4 C O_{2} (g)

Moles of

F e_{3} O_{4} = \frac{2.32 \times 1 0 ^{6} g}{232 g / m o l} = 1 0^{4} m o l

Moles of

C O = \frac{2.8 \times 1 0 ^{5} g}{28 g / m o l} = 1 0^{4} m o l

The stoichiometry requires 4 mol

C O

per mol

F e_{3} O_{4}

; only

1 0^{4}

mol

C O

is available against a demand of

4 \times 1 0^{4}

mol, so

C O

is the limiting reagent.

Moles of Fe produced

= \frac{3}{4} \times 1 0^{4} = 7500 m o l

Mass of Fe

= 7500 \times 56 = 4.2 \times 1 0^{5} g = 420 k g

JEE Main · 2025 · 24 Jan 2025 · Shift 1 · Integer answer